Let A = {n^2/2^n | n in N}. Find the supremum and infimum, proving your assertions.

Attempt at Solution

SupA:

The highest term in the set is 9/8 and thus it is the supremum, by definition.

InfA:

The terms in the set approach 0 as n becomes arbitrarily large. It is clear that 0 < n^2/2^n for all n, thus, 0 is a lower bound.

I'm not sure how to prove that 0 is the infimum. Can someone lead me in the right direction?